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We introduce the concept of maximum probability domains (MPDs), developed inthe context of the analysis of electronic densities, in the study of themicroscopic spatial structures of liquids. The idea of locating a particle in athree dimensional region, by determining the domain where the probability offinding that, and only that, particle is maximum, gives an interestingcharacterization of the local structure of the liquid. The optimizationprocedure, required for the search of the domain of maximum probability, iscarried out by the implementation of the level set method. Results for a coupleof case studies are presented, to illustrate the structure of liquid water atambient conditions and upon increasing pressure from the point of view of MPDsand to compare the information encoded in the solvation shells of sodium inwater with, once again, that extracted from the MPDs.

Maximum probability domains for the analysis of the microscopic structure of liquids